Had a similar problem on VR 6 cylinder Caprice. Good battery but just a tick, tick as if it were dead. Seemed like loose battery connection. Try again and eventually it will start. My son had the alternator replaced. It made no difference. New battery.. no difference. This went on for a number of months. Eventually, I got caught in a carpark. It wouldn't start no matter how long I waited before cranking again. I got the NRMA out and he correctly diagnosed a BAD EARTH STRAP. He said it was fairly common. Oh, and the car started by the time the NRMA came. The earth strap went front the inner guard to under the motor, near the oil filer from memory.
Grab an earth strap from the wrecker instead or get both it and the alternator if you want but make sure you can return the alternator.
Hope this does the trick for you.